1. Field of the Invention
The invention relates generally to the field of Earth formation electrical resistivity measuring devices. More particularly, the invention relates to wellbore instruments for measuring formation resistivity from within an electrically conductive pipe or casing including a moving while measuring apparatus and method.
2. Background Art
Electrical resistivity measurements of Earth formations are known in the art for determining properties of the measured Earth formations. Properties of interest include the fluid content of the pore spaces of the Earth formations. Wellbore resistivity measuring devices known in the art typically require that the Earth formations be exposed by drilling a wellbore therethrough, and that such formations remain exposed to the wellbore so that the measurements may be made from within the exposed formations.
When wellbores are completely drilled through the Earth formations of interest, frequently a steel pipe or casing is inserted into and cemented in place within the wellbore to protect the Earth formations, to prevent hydraulic communication between subsurface Earth formations, and to provide mechanical integrity to the wellbore. Steel casing is highly electrically conductive, and as a result makes it difficult to use conventional (so called “open hole”) techniques to determine the resistivity of the various Earth formations from within a steel pipe or casing.
It is known in the art to make measurements for determining the electrical resistivity of Earth formations from within conductive casing or pipe. A number of references disclose techniques for making such measurements. A list of references which disclose various apparatus and methods for determining resistivity of Earth formations from within conductive casings includes: USSR inventor certificate no. 56052, filed by Alpin, L. M. (1939), entitled, The method for logging in cased wells; USSR inventor certificate no. 56026, filed by Alpin, L. M. (1939), entitled, Process of the electrical measurement of well casing; U.S. Pat. No. 2,459,196, to Stewart, W. H. (1949), entitled, Electrical logging method and apparatus; U.S. Pat. No. 2,729,784 issued to Fearon, R. E. (1956), entitled, Method and apparatus for electric well logging, U.S. Pat. No. 2,891,215 issued to Fearon, R. E. (1959), entitled, Method and apparatus for electric well logging; French patent application no. 72.41218, filed by Desbrandes, R. and Mengez, P. (1972), entitled, Method & Apparatus for measuring the formation electrical resistivity in wells having metal casing; International Patent Application Publication no. WO 00/79307 A1, filed by Benimeli, D. (2002), entitled, A method and apparatus for determining of a formation surrounding a cased well; U.S. Pat. No. 4,796,186 issued to Kaufman, A. A. (1989), entitled, Conductivity determination in a formation having a cased well; U.S. Pat. No. 4,820,989, issued to Vail, III, W. (1989), entitled, Methods and apparatus for measurement of the resistivity of geological formation from within cased boreholes; U.S. Pat. No. 4,837,518 issued to Gard et al. (1989), entitled, Method and Apparatus for measuring the electrical resistivity of formation through metal drill pipe or casing; U.S. Pat. No. 4,882,542 issued to Vail, III, W. (1989), entitled, Methods and apparatus for measurement of electronic properties of geological formations through borehole casing; U.S. Pat. No. 5,043,668 issued to Vail, III, W. (1991), entitled, Methods and apparatus for measurement of electronic properties of geological formations through borehole casing; U.S. Pat. No. 5,075,626 issued to Vail, III, W. (1991), entitled, Electronic measurement apparatus movable in a cased borehole and compensation for casing resistance differences; U.S. Pat. No. 5,223,794 issued to Vail, III, W. (1993), entitled, Methods of apparatus measuring formation resistivity from within a cased well having one measurement and two compensation steps; U.S. Pat. No. 5,510,712 issued to Sezginer et al. (1996), entitled, Method and apparatus for measuring formation resistivity in cased holes; U.S. Pat. No. 5,543,715 issued to Singer et al. (1996), entitled, Method and apparatus for measuring formation resistivity through casing using single-conductor electrical logging cable; U.S. Pat. No. 5,563,514 issued to Moulin (1996), entitled, Method and apparatus for determining formation resistivity in a cased well using three electrodes arranged in a Wheatstone bridge. U.S. Pat. No. 5,654,639 issued to Locatelli et al. (1997), entitled, Induction measuring device in the presence of metal walls; U.S. Pat. No. 5,570,024 issued to Vail, III, W. (1996), entitled, Determining resistivity of a formation adjacent to a borehole having casing using multiple electrodes and resistances being defined between the electrodes; U.S. Pat. No. 5,608,323 issued to Koelman, J. M. V. A. (1997), entitled, Arrangement of the electrodes for an electrical logging system for determining the electrical resistivity of subsurface formation; U.S. Pat. No. 5,633,590 issued to Vail, III, W. (1997), entitled, Formation resistivity measurements from within a cased well used to quantitatively determine the amount of oil and gas present. U.S. Pat. No. 5,680,049 issued to Gissler et al. (1997), entitled, Apparatus for measuring formation resistivity through casing having a coaxial tubing inserted therein; U.S. Pat. No. 5,809,458 issued to Tamarchenko (1998), entitled, Method of simulating the response of a through-casing resistivity well logging instrument and its application to determining resistivity of earth formations; U.S. Pat. No. 6,025,721 issued to Vail, III, W. (2000), entitled, Determining resistivity of a formation adjacent to a borehole having casing by generating constant current flow in portion of casing and using at least two voltage measurement electrodes; U.S. Pat. No. 6,157,195 issued to Vail, III, W. (2000), entitled, Formation resistivity measurements from within a cased well used to quantitatively determine the amount of oil and gas present; U.S. Pat. No. 6,246,240 B1 issued to Vail, III, W. (2001), entitled, Determining resistivity of formation adjacent to a borehole having casing with an apparatus having all current conducting electrodes within the cased well; U.S. Pat. No. 6,603,314 issued to Kostelnicek et al. (2003), entitled, Simultaneous current injection for measurement of formation resistance through casing; and U.S. Pat. No. 6,667,621 issued to Benimelli, entitled, Method and apparatus for determining the resistivity of a formation surrounding a cased well. 
United States patent application Publications which cite relevant art include no. 2001/0033164 A1, filed by Vinegar et al., entitled, Focused through-casing resistivity measurement; no. 2001/0038287 A1, filed by Amini, Bijan K., entitled, Logging tool for measurement of resistivity through casing using metallic transparencies and magnetic lensing; no. 2002/0105333 A1 filed by Amini, Bijan K., entitled, Measurements of electrical properties through non magnetically permeable metals using directed magnetic beams and magnetic lenses. and no. 2003/0042016 A1, filed by Vinegar et al., entitled, Wireless communication using well casing 
The foregoing techniques are summarized briefly below. U.S. Pat. No. 2,459,196 describes a method for measuring inside a cased wellbore, whereby electrical current is caused to flow along the conductive casing such that some of the current will “leak” into the surrounding Earth formations. The amount of current leakage is related to the electrical conductivity of the Earth formations. The '196 patent does not disclose any technique for correcting the measurements for electrical inhomogeneities in the casing.
U.S. Pat. No. 2,729,784 discloses a technique in which three potential electrodes are used to create two opposed pairs of electrodes in contact with a wellbore casing. Electrical current is caused to flow in two opposing “loops” through two pairs of current electrodes placed above and below the potential electrodes such that electrical inhomogeneities in the casing have their effect nulled. Voltage drop across the two electrode pairs is related to the leakage current into the Earth formations. The disclosure in U.S. Pat. No. 2,891,215 includes a current emitter electrode disposed between the measuring electrodes of the apparatus disclosed in the '784 patent to provide a technique for fully compensating the leakage current.
U.S. Pat. No. 4,796,186 discloses the technique most frequently used to determine resistivity through conductive casing, and includes measuring leakage current into the Earth formations, and discloses measuring current flowing along the same portion of casing in which the leakage current is measured so as to compensate the measurements of leakage current for changes in resistance along the casing. Other references describe various extensions and improvements to the basic techniques of resistivity measurement through casing.
The methods known in the art for measuring resistivity through casing can be summarized as follows. An instrument is lowered into the wellbore having at least one electrode on the instrument (A) which is placed into contact with the casing at various depths in the casing. A casing current return electrode B is disposed at the top of and connected to the casing. A formation current return electrode B* is disposed at the Earth's surface at some distance from the wellbore. A record is made of the voltage drop and current flowing from electrode A in the wellbore at various depths, first to electrode B at the top of the casing and then to formation return electrode B*. Current flow and voltage drop through the casing (A-B) is used to correct measurements of voltage drop and current flow through the formation (A-B*) for effects of inhomogeneity in the casing.
If the Earth and the casing were both homogeneous, a record with respect to depth of the voltage drop along the casing, and the voltage drop through the casing and formation, would be substantially linear. As is well known in the art, casing includes inhomogeneities, even when new, resulting from construction tolerances, composition tolerances, and even “collars” (threaded couplings) used to connect segments of the casing to each other. Earth formations, of course, are not at all homogeneous, and more resistive formations are typically the object of subsurface investigation, because these Earth formations tend to be associated with presence of petroleum, while the more conductive formations tend to be associated with the presence of all connate water in the pore spaces. Therefore, it is the perturbations in the record of voltage drop with respect to depth that are of interest in determining resistivity of Earth formations outside casing using the techniques known in the art.
The conductivity of the Earth formations is related to the amount of current leaking out of the casing into the formations. The formation conductivity with respect to depth is generally related to the second derivative of the voltage drop along A-B with respect to depth, when current is flowing between A and B*. Typically, the second derivative of the voltage drop is measured using a minimum of three axially spaced apart electrodes placed in contact with the casing, coupled to cascaded differential amplifiers, ultimately coupled to a voltage measuring circuit. Improvements to the basic method that have proven useful include systems which create s small axial zone along the casing in which substantially no current flows along the casing itself to reduce the effects of casing inhomogeneity on the measurements of leakage current voltage drop.
In practice, instruments and methods known in the art require that the instrument make its measurements from a fixed position within the wellbore, which makes measuring formations of interest penetrated by a typical wellbore take an extensive amount of time. Further, the voltage drops being measured are small, and thus subject to noise limitations of the electronic systems used to make the measurements of voltage drop. Still further, systems known in the art for providing no-current zones, or known current flow values for measurements of voltage drop, are typically analog systems, and thus subject to the accuracy limitations of such analog systems.
Still further, it is known in the art to use low frequency alternating current (AC) to induce current flow along the casing and in the Earth formations. AC is used to avoid error resulting from electrical polarization of the casing and the electrodes when continuous direct current (DC) is used. Typically, the frequency of the AC must be limited to about 0.01 to 20 Hz to avoid error in the measurements caused by dielectric effects and the skin effect. It is also known in the art to use polarity-switched DC to make through casing resistivity measurements, which avoids the polarization problem, but may induce transient effect error in the measurements when the DC polarity is switched. Transient effects, and low frequency AC errors are not easily accounted for using systems known in the art.
Lastly, it is known in the art to simulate response of a through-casing resistivity measuring instrument. See, for example, U.S. Pat. No. 5,809,458 issued to Tamarchenko (1998), entitled, Method of simulating the response of a through-casing resistivity well logging instrument and its application to determining resistivity of earth formations. In a process for determining resistivity of formations from within a conductive pipe or casing as disclosed in the Tamarchenko '458 patent, an initial model of Earth formations is made, and the expected response of a resistivity measurement device is simulated. The simulated response is compared to the response actually measured by the instrument. The model is adjusted, and the simulation and comparison are repeated until differences between the simulated response and the measured response reach a minimum. When the differences reach a minimum, the model extant at that point is determined to represent the spatial distribution of resistivities in the Earth surrounding the conductive pipe or casing. While the method of the '458 patent is effective, it can be computationally intensive to perform, because voltage measurements from the resistivity measurement systems known in the art for measuring resistivity from within a conductive casing are extremely complex, and the number of possible Earth models which can be consistent with the measured response may cause initializing the Earth model to be time consuming. What is needed is an instrument for measuring resistivity through a conductive pipe or casing that includes measurements capable of efficiently constraining the initial Earth model so that subsequent inversion processing more quickly converges on a solution model.